The radius of a sphere is $p$ units and the radius of a hemisphere is $2p$ units. What is the ratio of the volume of the sphere to the volume of the hemisphere?
Explanation: The volume of the sphere is \[\frac{4}{3}\pi p^3\] and the volume of the hemisphere is \[\frac{1}{2}\cdot \frac{4}{3}\pi (2p)^3 = \frac{4}{3}\pi p^3 \cdot 4.\] Thus the ratio of the volume of the sphere to the volume of the hemisphere is $\boxed{\frac{1}{4}}$.